Related papers: Phase Transitions in Nonlinear Filtering

We study the periodic properties of sequences of quantum channels sampled from an ergodic stochastic process satisfying a natural irreducibility condition. We relate these periodic properties to certain global spectral data defined by the…

We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…

Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…

A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper. The existence of an exponentially…

We develop a Perron-Frobenius type theory for products of random quantum channels acting on finite-dimensional matrix algebras sampled from a stationary and ergodic stochastic process, which, in keeping with the literature, we call ergodic…

We consider the ergodicity and consensus problem for a discrete-time linear dynamic model driven by random stochastic matrices, which is equivalent to studying these concepts for the product of such matrices. Our focus is on the model where…

We study a one parameter family of random graph models that spans a continuum between traditional random graphs of the Erd\H{o}s-R\'enyi type, where there is no underlying structure, and percolation models, where the possible edges are…

I present an analytic approach to establishing the presence of phase transitions in a large set of decision problems. This approach does not require extensive computational study of the problems considered. The set -- that of all paddable…

We study nonlinear Neumann type boundary value problems related to ergodic phenomenas. The particularity of these problems is that the ergodic constant appears in the (possibly nonlinear) Neumann boundary conditions. We provide, for bounded…

We investigate one-dimensional driven diffusive systems where particles may also be created and annihilated in the bulk with sufficiently small rate. In an open geometry, i.e., coupled to particle reservoirs at the two ends, these systems…

Using a model Hamiltonian for a single-mode electromagnetic field interacting with a nonlinear medium, we show that quantum expectation values of subsystem observables can exhibit remarkably diverse ergodic properties even when the dynamics…

Motivated by a model presented by S. Gudder, we study a quantum generalization of Markov chains and discuss the relation between these maps and open quantum random walks, a class of quantum channels described by S. Attal et al. We consider…

This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes with Incomplete Information and with semi-uniform Feller transition probabilities. The important…

In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…

We describe the full exit boundary of random walks on homogeneous trees, in particular, on the free groups. This model exhibits a phase transition, namely, the family of Markov measures under study loses ergodicity as a parameter of the…

Stability problem of the Wonham filter with respect to initial conditions is addressed. The case of ergodic signals is revisited in view of a gap in the classic work of H. Kunita (1971). We give new bounds for the exponential stability…

The present paper has two goals. First to present a natural example of a new class of random fields which are the variable neighborhood random fields. The example we consider is a partially observed nearest neighbor binary Markov random…

We study a general class of random walks driven by a uniquely ergodic Markovian environment. Under a coupling condition on the environment we obtain strong ergodicity properties for the environment as seen from the position of the walker,…

We present examples of queuing networks that never come to equilibrium. That is achieved by constructing Non-linear Markov Processes, which are non-ergodic, and possess eternal transience property.

Ergodicity is a fundamental issue for a stochastic process. In this paper, we refine results on ergodicity for a general type of Markov chain to a specific type or the $GI/G/1$-type Markov chain, which has many interesting and important…